Question 9535
Divide cubic polynomial by x - 1

The quotient is x^2 -2x + 2

The cubic equation factors into

 (x-1)(x^2 -2x + 2) = 0

 We already know that x=1 is a root
The other roots are obtained by solving 

 x^2 -2x + 2 = 0

  This can be written

 (x-1)^2 + 1 = 0

 (x-1)^2 = -1

 x-1 = i or x-1 = -i where i is square root of -1

 x = 1 + i or x = 1 - i

The zeros of h(x)=x^3-3x^2+4x-2

 are 1,1 + i, 1 - i

To find zeros of f(x) = x^4 -10x^2 + 24

 We factor x^4 -10x^2 + 24

 x^4 -10x^2 + 24 = (x^2 -4)(x^2-6)

                 = (x-2)(x+2)(x^2 - 6)

   then solve

(x-2)(x+2)(x^2 - 6) = 0

 By setting each factor equal to 0 and solving for x

 x=2,or x=-2,or x=-sqrt 6,or x=sqrt 6
These are the zeros of f(x)